Adaptive Local Mesh Refinement in 2-D Finite Volume Method for Steady State and Transient Simulations of Semiconductor Devices

An adaptive nonconforming mesh refinement technique for 2-D semiconductor device simulations with the finite volume scheme on triangular meshes is proposed to enhance the numerical accuracy in regions of interest. To capture the solution with large gradients in thin layers, three physics-based cell refinement indicators are proposed to effectively locate the critical areas near the junctions, electrodes, and the boundaries of depletion regions, respectively. The local conservation property of the finite volume Scharfetter-Gummel (FVSG) scheme is preserved in refined cells by a proper control volume discretization for meshes even with hanging nodes. Steady state and transient simulations of semiconductors demonstrated that the numerical error is effectively reduced and computational burden is relieved by the proposed method.